LMFDB - Embedded newform 231.2.g.a.197.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(197,231)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.10
Character	$\chi$	$=$	231.197
Dual form			231.2.g.a.197.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.858468 q^{2} +(1.60964 + 0.639565i) q^{3} -1.26303 q^{4} +2.44714i q^{5} +(-1.38183 - 0.549047i) q^{6} -1.00000i q^{7} +2.80121 q^{8} +(2.18191 + 2.05895i) q^{9} +O(q^{10})$	\(q-0.858468 q^{2} +(1.60964 + 0.639565i) q^{3} -1.26303 q^{4} +2.44714i q^{5} +(-1.38183 - 0.549047i) q^{6} -1.00000i q^{7} +2.80121 q^{8} +(2.18191 + 2.05895i) q^{9} -2.10079i q^{10} +(-3.19676 + 0.883578i) q^{11} +(-2.03303 - 0.807792i) q^{12} +5.20778i q^{13} +0.858468i q^{14} +(-1.56511 + 3.93903i) q^{15} +0.121314 q^{16} +0.151573 q^{17} +(-1.87310 - 1.76754i) q^{18} +3.38435i q^{19} -3.09082i q^{20} +(0.639565 - 1.60964i) q^{21} +(2.74432 - 0.758524i) q^{22} -5.75973i q^{23} +(4.50895 + 1.79156i) q^{24} -0.988494 q^{25} -4.47072i q^{26} +(2.19527 + 4.70965i) q^{27} +1.26303i q^{28} +6.48993 q^{29} +(1.34359 - 3.38153i) q^{30} -5.46192 q^{31} -5.70656 q^{32} +(-5.71076 - 0.622291i) q^{33} -0.130121 q^{34} +2.44714 q^{35} +(-2.75583 - 2.60052i) q^{36} +7.70173 q^{37} -2.90535i q^{38} +(-3.33072 + 8.38268i) q^{39} +6.85495i q^{40} +2.83876 q^{41} +(-0.549047 + 1.38183i) q^{42} -9.44759i q^{43} +(4.03761 - 1.11599i) q^{44} +(-5.03853 + 5.33944i) q^{45} +4.94454i q^{46} -0.242178i q^{47} +(0.195273 + 0.0775883i) q^{48} -1.00000 q^{49} +0.848591 q^{50} +(0.243979 + 0.0969411i) q^{51} -6.57760i q^{52} -11.3416i q^{53} +(-1.88457 - 4.04308i) q^{54} +(-2.16224 - 7.82293i) q^{55} -2.80121i q^{56} +(-2.16451 + 5.44759i) q^{57} -5.57140 q^{58} +2.22046i q^{59} +(1.97678 - 4.97512i) q^{60} -11.1592i q^{61} +4.68888 q^{62} +(2.05895 - 2.18191i) q^{63} +4.65628 q^{64} -12.7442 q^{65} +(4.90250 + 0.534218i) q^{66} -1.94205 q^{67} -0.191442 q^{68} +(3.68372 - 9.27111i) q^{69} -2.10079 q^{70} -7.57130i q^{71} +(6.11199 + 5.76754i) q^{72} +3.49122i q^{73} -6.61169 q^{74} +(-1.59112 - 0.632207i) q^{75} -4.27454i q^{76} +(0.883578 + 3.19676i) q^{77} +(2.85932 - 7.19627i) q^{78} +11.6311i q^{79} +0.296873i q^{80} +(0.521482 + 8.98488i) q^{81} -2.43699 q^{82} +15.6670 q^{83} +(-0.807792 + 2.03303i) q^{84} +0.370921i q^{85} +8.11046i q^{86} +(10.4465 + 4.15073i) q^{87} +(-8.95480 + 2.47509i) q^{88} -2.58238i q^{89} +(4.32542 - 4.58374i) q^{90} +5.20778 q^{91} +7.27472i q^{92} +(-8.79175 - 3.49325i) q^{93} +0.207902i q^{94} -8.28197 q^{95} +(-9.18554 - 3.64972i) q^{96} -5.06076 q^{97} +0.858468 q^{98} +(-8.79429 - 4.65407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.858468			−0.607029			−0.303514	−	0.952827i	$-0.598160\pi$
$2$	−0.858468			−0.607029			−0.303514	+	0.952827i	$0.598160\pi$
$3$	1.60964	+	0.639565i	0.929329	+	0.369253i
$3$	1.60964	+	0.639565i	0.929329	+	0.369253i
$4$	−1.26303			−0.631516
$5$			2.44714i			1.09439i	0.837004	+	0.547197i	$0.184305\pi$
$5$			2.44714i			1.09439i	−0.837004	+	0.547197i	$0.815695\pi$
$6$	−1.38183	−	0.549047i	−0.564129	−	0.224147i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.80121			0.990377
$9$	2.18191	+	2.05895i	0.727304	+	0.686315i
$10$		−	2.10079i		−	0.664329i
$11$	−3.19676	+	0.883578i	−0.963860	+	0.266409i
$11$	−3.19676	+	0.883578i	−0.963860	+	0.266409i
$12$	−2.03303	−	0.807792i	−0.586886	−	0.233189i
$13$			5.20778i			1.44438i	0.691695	+	0.722190i	$0.256864\pi$
$13$			5.20778i			1.44438i	−0.691695	+	0.722190i	$0.743136\pi$
$14$			0.858468i			0.229435i
$15$	−1.56511	+	3.93903i	−0.404109	+	1.01705i
$16$	0.121314			0.0303285
$17$	0.151573			0.0367619			0.0183810	−	0.999831i	$-0.494149\pi$
$17$	0.151573			0.0367619			0.0183810	+	0.999831i	$0.494149\pi$
$18$	−1.87310	−	1.76754i	−0.441495	−	0.416613i
$19$			3.38435i			0.776422i	0.921570	+	0.388211i	$0.126907\pi$
$19$			3.38435i			0.776422i	−0.921570	+	0.388211i	$0.873093\pi$
$20$		−	3.09082i		−	0.691128i
$21$	0.639565	−	1.60964i	0.139565	−	0.351253i
$22$	2.74432	−	0.758524i	0.585091	−	0.161718i
$23$		−	5.75973i		−	1.20099i	−0.799630	−	0.600493i	$-0.794971\pi$
$23$		−	5.75973i		−	1.20099i	0.799630	−	0.600493i	$-0.205029\pi$
$24$	4.50895	+	1.79156i	0.920386	+	0.365700i
$25$	−0.988494			−0.197699
$26$		−	4.47072i		−	0.876780i
$27$	2.19527	+	4.70965i	0.422480	+	0.906372i
$28$			1.26303i			0.238691i
$29$	6.48993			1.20515			0.602575	−	0.798062i	$-0.294142\pi$
$29$	6.48993			1.20515			0.602575	+	0.798062i	$0.294142\pi$
$30$	1.34359	−	3.38153i	0.245306	−	0.617380i
$31$	−5.46192			−0.980989			−0.490495	−	0.871444i	$-0.663184\pi$
$31$	−5.46192			−0.980989			−0.490495	+	0.871444i	$0.663184\pi$
$32$	−5.70656			−1.00879
$33$	−5.71076	−	0.622291i	−0.994115	−	0.108327i
$34$	−0.130121			−0.0223156
$35$	2.44714			0.413642
$36$	−2.75583	−	2.60052i	−0.459304	−	0.433419i
$37$	7.70173			1.26616			0.633078	−	0.774088i	$-0.281791\pi$
$37$	7.70173			1.26616			0.633078	+	0.774088i	$0.281791\pi$
$38$		−	2.90535i		−	0.471311i
$39$	−3.33072	+	8.38268i	−0.533342	+	1.34230i
$40$			6.85495i			1.08386i
$41$	2.83876			0.443340			0.221670	−	0.975122i	$-0.428849\pi$
$41$	2.83876			0.443340			0.221670	+	0.975122i	$0.428849\pi$
$42$	−0.549047	+	1.38183i	−0.0847197	+	0.213221i
$43$		−	9.44759i		−	1.44074i	−0.693588	−	0.720372i	$-0.743971\pi$
$43$		−	9.44759i		−	1.44074i	0.693588	−	0.720372i	$-0.256029\pi$
$44$	4.03761	−	1.11599i	0.608693	−	0.168241i
$45$	−5.03853	+	5.33944i	−0.751100	+	0.795957i
$46$			4.94454i			0.729033i
$47$		−	0.242178i		−	0.0353252i	−0.999844	−	0.0176626i	$-0.994378\pi$
$47$		−	0.242178i		−	0.0353252i	0.999844	−	0.0176626i	$-0.00562248\pi$
$48$	0.195273	+	0.0775883i	0.0281852	+	0.0111989i
$49$	−1.00000			−0.142857
$50$	0.848591			0.120009
$51$	0.243979	+	0.0969411i	0.0341639	+	0.0135745i
$52$		−	6.57760i		−	0.912149i
$53$		−	11.3416i		−	1.55789i	−0.627091	−	0.778946i	$-0.715754\pi$
$53$		−	11.3416i		−	1.55789i	0.627091	−	0.778946i	$-0.284246\pi$
$54$	−1.88457	−	4.04308i	−0.256458	−	0.550194i
$55$	−2.16224	−	7.82293i	−0.291556	−	1.05484i
$56$		−	2.80121i		−	0.374327i
$57$	−2.16451	+	5.44759i	−0.286696	+	0.721552i
$58$	−5.57140			−0.731560
$59$			2.22046i			0.289080i	0.989499	+	0.144540i	$0.0461702\pi$
$59$			2.22046i			0.289080i	−0.989499	+	0.144540i	$0.953830\pi$
$60$	1.97678	−	4.97512i	0.255201	−	0.642285i
$61$		−	11.1592i		−	1.42879i	−0.699741	−	0.714397i	$-0.746701\pi$
$61$		−	11.1592i		−	1.42879i	0.699741	−	0.714397i	$-0.253299\pi$
$62$	4.68888			0.595489
$63$	2.05895	−	2.18191i	0.259403	−	0.274895i
$64$	4.65628			0.582035
$65$	−12.7442			−1.58072
$66$	4.90250	+	0.534218i	0.603457	+	0.0657576i
$67$	−1.94205			−0.237259			−0.118630	−	0.992939i	$-0.537850\pi$
$67$	−1.94205			−0.237259			−0.118630	+	0.992939i	$0.537850\pi$
$68$	−0.191442			−0.0232157
$69$	3.68372	−	9.27111i	0.443468	−	1.11611i
$70$	−2.10079			−0.251093
$71$		−	7.57130i		−	0.898548i	−0.893394	−	0.449274i	$-0.851683\pi$
$71$		−	7.57130i		−	0.898548i	0.893394	−	0.449274i	$-0.148317\pi$
$72$	6.11199	+	5.76754i	0.720305	+	0.679711i
$73$			3.49122i			0.408616i	0.978907	+	0.204308i	$0.0654945\pi$
$73$			3.49122i			0.408616i	−0.978907	+	0.204308i	$0.934506\pi$
$74$	−6.61169			−0.768593
$75$	−1.59112	−	0.632207i	−0.183727	−	0.0730009i
$76$		−	4.27454i		−	0.490323i
$77$	0.883578	+	3.19676i	0.100693	+	0.364305i
$78$	2.85932	−	7.19627i	0.323754	−	0.814817i
$79$			11.6311i			1.30861i	0.756232	+	0.654303i	$0.227038\pi$
$79$			11.6311i			1.30861i	−0.756232	+	0.654303i	$0.772962\pi$
$80$			0.296873i			0.0331914i
$81$	0.521482	+	8.98488i	0.0579424	+	0.998320i
$82$	−2.43699			−0.269120
$83$	15.6670			1.71968			0.859841	−	0.510562i	$-0.170563\pi$
$83$	15.6670			1.71968			0.859841	+	0.510562i	$0.170563\pi$
$84$	−0.807792	+	2.03303i	−0.0881373	+	0.221822i
$85$			0.370921i			0.0402320i
$86$			8.11046i			0.874574i
$87$	10.4465	+	4.15073i	1.11998	+	0.445005i
$88$	−8.95480	+	2.47509i	−0.954585	+	0.263845i
$89$		−	2.58238i		−	0.273732i	−0.990590	−	0.136866i	$-0.956297\pi$
$89$		−	2.58238i		−	0.273732i	0.990590	−	0.136866i	$-0.0437030\pi$
$90$	4.32542	−	4.58374i	0.455939	−	0.483169i
$91$	5.20778			0.545924
$92$			7.27472i			0.758442i
$93$	−8.79175	−	3.49325i	−0.911662	−	0.362234i
$94$			0.207902i			0.0214434i
$95$	−8.28197			−0.849712
$96$	−9.18554	−	3.64972i	−0.937495	−	0.372498i
$97$	−5.06076			−0.513842			−0.256921	−	0.966432i	$-0.582708\pi$
$97$	−5.06076			−0.513842			−0.256921	+	0.966432i	$0.582708\pi$
$98$	0.858468			0.0867184
$99$	−8.79429	−	4.65407i	−0.883860	−	0.467752i
$100$	1.24850			0.124850
$101$	2.97195			0.295720			0.147860	−	0.989008i	$-0.452762\pi$
$101$	2.97195			0.295720			0.147860	+	0.989008i	$0.452762\pi$
$102$	−0.209448	−	0.0832208i	−0.0207385	−	0.00824009i
$103$	2.10711			0.207620			0.103810	−	0.994597i	$-0.466897\pi$
$103$	2.10711			0.207620			0.103810	+	0.994597i	$0.466897\pi$
$104$			14.5881i			1.43048i
$105$	3.93903	+	1.56511i	0.384410	+	0.152739i
$106$			9.73643i			0.945686i
$107$	−15.5706			−1.50527			−0.752635	−	0.658438i	$-0.771218\pi$
$107$	−15.5706			−1.50527			−0.752635	+	0.658438i	$0.771218\pi$
$108$	−2.77270	−	5.94844i	−0.266803	−	0.572388i
$109$		−	4.19595i		−	0.401899i	−0.979602	−	0.200950i	$-0.935597\pi$
$109$		−	4.19595i		−	0.401899i	0.979602	−	0.200950i	$-0.0644027\pi$
$110$	1.85621	+	6.71573i	0.176983	+	0.640320i
$111$	12.3970	+	4.92576i	1.17668	+	0.467532i
$112$		−	0.121314i		−	0.0114631i
$113$			18.7645i			1.76521i	0.470113	+	0.882606i	$0.344213\pi$
$113$			18.7645i			1.76521i	−0.470113	+	0.882606i	$0.655787\pi$
$114$	1.85816	−	4.67659i	0.174033	−	0.438003i
$115$	14.0949			1.31435
$116$	−8.19699			−0.761071
$117$	−10.7225	+	11.3629i	−0.991300	+	1.05050i
$118$		−	1.90620i		−	0.175480i
$119$		−	0.151573i		−	0.0138947i
$120$	−4.38419	+	11.0340i	−0.400220	+	1.00727i
$121$	9.43858	−	5.64918i	0.858053	−	0.513562i
$122$			9.57985i			0.867319i
$123$	4.56940	+	1.81557i	0.412009	+	0.163705i
$124$	6.89858			0.619511
$125$			9.81672i			0.878034i
$126$	−1.76754	+	1.87310i	−0.157465	+	0.166869i
$127$			0.108701i			0.00964569i	0.999988	+	0.00482284i	$0.00153516\pi$
$127$			0.108701i			0.00964569i	−0.999988	+	0.00482284i	$0.998465\pi$
$128$	7.41586			0.655476
$129$	6.04235	−	15.2073i	0.532000	−	1.33893i
$130$	10.9405			0.959543
$131$	12.8269			1.12069			0.560347	−	0.828258i	$-0.310668\pi$
$131$	12.8269			1.12069			0.560347	+	0.828258i	$0.310668\pi$
$132$	7.21287	+	0.785974i	0.627800	+	0.0684103i
$133$	3.38435			0.293460
$134$	1.66719			0.144023
$135$	−11.5252	+	5.37214i	−0.991928	+	0.462360i
$136$	0.424589			0.0364082
$137$			17.6915i			1.51149i	0.654868	+	0.755743i	$0.272724\pi$
$137$			17.6915i			1.51149i	−0.654868	+	0.755743i	$0.727276\pi$
$138$	−3.16236	+	7.95896i	−0.269198	+	0.677511i
$139$			2.19619i			0.186278i	0.995653	+	0.0931391i	$0.0296901\pi$
$139$			2.19619i			0.186278i	−0.995653	+	0.0931391i	$0.970310\pi$
$140$	−3.09082			−0.261222
$141$	0.154888	−	0.389820i	0.0130440	−	0.0328287i
$142$			6.49972i			0.545445i
$143$	−4.60148	−	16.6480i	−0.384795	−	1.39218i
$144$	0.264697	+	0.249779i	0.0220581	+	0.0208149i
$145$			15.8818i			1.31891i
$146$		−	2.99710i		−	0.248042i
$147$	−1.60964	−	0.639565i	−0.132761	−	0.0527505i
$148$	−9.72753			−0.799598
$149$	−7.83843			−0.642149			−0.321075	−	0.947054i	$-0.604044\pi$
$149$	−7.83843			−0.642149			−0.321075	+	0.947054i	$0.604044\pi$
$150$	1.36593	+	0.542729i	0.111528	+	0.0443137i
$151$		−	8.21629i		−	0.668632i	−0.942461	−	0.334316i	$-0.891495\pi$
$151$		−	8.21629i		−	0.668632i	0.942461	−	0.334316i	$-0.108505\pi$
$152$			9.48026i			0.768951i
$153$	0.330720	+	0.312081i	0.0267371	+	0.0252303i
$154$	−0.758524	−	2.74432i	−0.0611236	−	0.221144i
$155$		−	13.3661i		−	1.07359i
$156$	4.20680	−	10.5876i	0.336814	−	0.847686i
$157$	9.44050			0.753434			0.376717	−	0.926328i	$-0.377053\pi$
$157$	9.44050			0.753434			0.376717	+	0.926328i	$0.377053\pi$
$158$		−	9.98497i		−	0.794362i
$159$	7.25371	−	18.2560i	0.575257	−	1.44779i
$160$		−	13.9648i		−	1.10401i
$161$	−5.75973			−0.453930
$162$	−0.447675	−	7.71323i	−0.0351727	−	0.606009i
$163$	−8.13501			−0.637183			−0.318591	−	0.947892i	$-0.603210\pi$
$163$	−8.13501			−0.637183			−0.318591	+	0.947892i	$0.603210\pi$
$164$	−3.58545			−0.279976
$165$	1.52283	−	13.9750i	0.118552	−	1.08795i
$166$	−13.4497			−1.04390
$167$	2.64732			0.204856			0.102428	−	0.994740i	$-0.467339\pi$
$167$	2.64732			0.204856			0.102428	+	0.994740i	$0.467339\pi$
$168$	1.79156	−	4.50895i	0.138222	−	0.347873i
$169$	−14.1210			−1.08623
$170$		−	0.318424i		−	0.0244220i
$171$	−6.96819	+	7.38435i	−0.532871	+	0.564695i
$172$			11.9326i			0.909853i
$173$	−3.03157			−0.230486			−0.115243	−	0.993337i	$-0.536765\pi$
$173$	−3.03157			−0.230486			−0.115243	+	0.993337i	$0.536765\pi$
$174$	−8.96797	−	3.56327i	−0.679860	−	0.270131i
$175$			0.988494i			0.0747231i
$176$	−0.387812	+	0.107191i	−0.0292325	+	0.00807979i
$177$	−1.42013	+	3.57416i	−0.106744	+	0.268650i
$178$			2.21689i			0.166163i
$179$		−	9.79967i		−	0.732462i	−0.930524	−	0.366231i	$-0.880648\pi$
$179$		−	9.79967i		−	0.732462i	0.930524	−	0.366231i	$-0.119352\pi$
$180$	6.36382	−	6.74389i	0.474331	−	0.502660i
$181$	−8.03062			−0.596911			−0.298456	−	0.954424i	$-0.596471\pi$
$181$	−8.03062			−0.596911			−0.298456	+	0.954424i	$0.596471\pi$
$182$	−4.47072			−0.331392
$183$	7.13706	−	17.9624i	0.527587	−	1.32782i
$184$		−	16.1342i		−	1.18943i
$185$			18.8472i			1.38567i
$186$	7.54744	+	2.99885i	0.553405	+	0.219886i
$187$	−0.484544	+	0.133927i	−0.0354334	+	0.00979370i
$188$			0.305878i			0.0223084i
$189$	4.70965	−	2.19527i	0.342576	−	0.159683i
$190$	7.10981			0.515800
$191$		−	19.1519i		−	1.38578i	−0.721042	−	0.692892i	$-0.756336\pi$
$191$		−	19.1519i		−	1.38578i	0.721042	−	0.692892i	$-0.243664\pi$
$192$	7.49495	+	2.97799i	0.540901	+	0.214918i
$193$			0.410169i			0.0295246i	0.999891	+	0.0147623i	$0.00469916\pi$
$193$			0.410169i			0.0295246i	−0.999891	+	0.0147623i	$0.995301\pi$
$194$	4.34450			0.311917
$195$	−20.5136	−	8.15073i	−1.46901	−	0.583686i
$196$	1.26303			0.0902166
$197$	14.6387			1.04297			0.521483	−	0.853262i	$-0.325379\pi$
$197$	14.6387			1.04297			0.521483	+	0.853262i	$0.325379\pi$
$198$	7.54962	+	3.99537i	0.536528	+	0.283939i
$199$	−25.7403			−1.82468			−0.912342	−	0.409430i	$-0.865728\pi$
$199$	−25.7403			−1.82468			−0.912342	+	0.409430i	$0.865728\pi$
$200$	−2.76898			−0.195796
$201$	−3.12601	−	1.24207i	−0.220492	−	0.0876088i
$202$	−2.55132			−0.179510
$203$		−	6.48993i		−	0.455504i
$204$	−0.308154	−	0.122440i	−0.0215751	−	0.00857249i
$205$			6.94685i			0.485189i
$206$	−1.80889			−0.126031
$207$	11.8590	−	12.5672i	0.824255	−	0.873482i
$208$			0.631778i			0.0438059i
$209$	−2.99033	−	10.8190i	−0.206846	−	0.748362i
$210$	−3.38153	−	1.34359i	−0.233348	−	0.0927168i
$211$			15.4265i			1.06200i	0.847371	+	0.531001i	$0.178184\pi$
$211$			15.4265i			1.06200i	−0.847371	+	0.531001i	$0.821816\pi$
$212$			14.3248i			0.983834i
$213$	4.84234	−	12.1871i	0.331792	−	0.835047i
$214$	13.3669			0.913743
$215$	23.1196			1.57674
$216$	6.14942	+	13.1927i	0.418415	+	0.897650i
$217$			5.46192i			0.370779i
$218$			3.60209i			0.243964i
$219$	−2.23286	+	5.61962i	−0.150883	+	0.379739i
$220$	2.73098	+	9.88061i	0.184123	+	0.666150i
$221$			0.789361i			0.0530982i
$222$	−10.6425	−	4.22861i	−0.714276	−	0.283806i
$223$	−17.9823			−1.20419			−0.602094	−	0.798426i	$-0.705667\pi$
$223$	−17.9823			−1.20419			−0.602094	+	0.798426i	$0.705667\pi$
$224$			5.70656i			0.381286i
$225$	−2.15681	−	2.03526i	−0.143787	−	0.135684i
$226$		−	16.1087i		−	1.07153i
$227$	13.2902			0.882102			0.441051	−	0.897482i	$-0.354606\pi$
$227$	13.2902			0.882102			0.441051	+	0.897482i	$0.354606\pi$
$228$	2.73385	−	6.88049i	0.181053	−	0.455671i
$229$	19.3202			1.27671			0.638356	−	0.769741i	$-0.279615\pi$
$229$	19.3202			1.27671			0.638356	+	0.769741i	$0.279615\pi$
$230$	−12.1000			−0.797850
$231$	−0.622291	+	5.71076i	−0.0409438	+	0.375740i
$232$	18.1797			1.19355
$233$	−4.43936			−0.290832			−0.145416	−	0.989371i	$-0.546452\pi$
$233$	−4.43936			−0.290832			−0.145416	+	0.989371i	$0.546452\pi$
$234$	9.20497	−	9.75471i	0.601747	−	0.637686i
$235$	0.592642			0.0386597
$236$		−	2.80452i		−	0.182558i
$237$	−7.43888	+	18.7220i	−0.483207	+	1.21613i
$238$			0.130121i			0.00843449i
$239$	1.39522			0.0902494			0.0451247	−	0.998981i	$-0.485631\pi$
$239$	1.39522			0.0902494			0.0451247	+	0.998981i	$0.485631\pi$
$240$	−0.189869	+	0.477860i	−0.0122560	+	0.0308457i
$241$		−	15.3983i		−	0.991894i	−0.868353	−	0.495947i	$-0.834821\pi$
$241$		−	15.3983i		−	0.991894i	0.868353	−	0.495947i	$-0.165179\pi$
$242$	−8.10272	+	4.84964i	−0.520863	+	0.311747i
$243$	−4.90702	+	14.7960i	−0.314785	+	0.949163i
$244$			14.0945i			0.902306i
$245$		−	2.44714i		−	0.156342i
$246$	−3.92268	−	1.55861i	−0.250101	−	0.0993735i
$247$	−17.6249			−1.12145
$248$	−15.3000			−0.971550
$249$	25.2184	+	10.0201i	1.59815	+	0.634998i
$250$		−	8.42734i		−	0.532992i
$251$		−	20.8877i		−	1.31842i	−0.751958	−	0.659211i	$-0.770890\pi$
$251$		−	20.8877i		−	1.31842i	0.751958	−	0.659211i	$-0.229110\pi$
$252$	−2.60052	+	2.75583i	−0.163817	+	0.173601i
$253$	5.08917	+	18.4125i	0.319953	+	1.15758i
$254$		−	0.0933167i		−	0.00585521i
$255$	−0.237228	+	0.597051i	−0.0148558	+	0.0373888i
$256$	−15.6788			−0.979927
$257$			7.35614i			0.458863i	0.973325	+	0.229432i	$0.0736867\pi$
$257$			7.35614i			0.458863i	−0.973325	+	0.229432i	$0.926313\pi$
$258$	−5.18717	+	13.0550i	−0.322939	+	0.812766i
$259$		−	7.70173i		−	0.478562i
$260$	16.0963			0.998250
$261$	14.1605	+	13.3624i	0.876510	+	0.827113i
$262$	−11.0115			−0.680293
$263$	0.993296			0.0612493			0.0306246	−	0.999531i	$-0.490250\pi$
$263$	0.993296			0.0612493			0.0306246	+	0.999531i	$0.490250\pi$
$264$	−15.9970	−	1.74317i	−0.984549	−	0.107285i
$265$	27.7546			1.70495
$266$	−2.90535			−0.178139
$267$	1.65160	−	4.15672i	0.101076	−	0.254387i
$268$	2.45287			0.149833
$269$		−	13.9465i		−	0.850333i	−0.905115	−	0.425167i	$-0.860215\pi$
$269$		−	13.9465i		−	0.850333i	0.905115	−	0.425167i	$-0.139785\pi$
$270$	9.89399	−	4.61181i	0.602129	−	0.280666i
$271$		−	31.1174i		−	1.89025i	−0.326709	−	0.945125i	$-0.605940\pi$
$271$		−	31.1174i		−	1.89025i	0.326709	−	0.945125i	$-0.394060\pi$
$272$	0.0183880			0.00111494
$273$	8.38268	+	3.33072i	0.507343	+	0.201584i
$274$		−	15.1876i		−	0.917516i
$275$	3.15998	−	0.873412i	0.190554	−	0.0526687i
$276$	−4.65266	+	11.7097i	−0.280057	+	0.704842i
$277$		−	8.65778i		−	0.520195i	−0.965582	−	0.260098i	$-0.916245\pi$
$277$		−	8.65778i		−	0.520195i	0.965582	−	0.260098i	$-0.0837548\pi$
$278$		−	1.88536i		−	0.113076i
$279$	−11.9174	−	11.2458i	−0.713478	−	0.673268i
$280$	6.85495			0.409662
$281$	−26.3528			−1.57208			−0.786038	−	0.618178i	$-0.787871\pi$
$281$	−26.3528			−1.57208			−0.786038	+	0.618178i	$0.787871\pi$
$282$	−0.132967	+	0.334648i	−0.00791806	+	0.0199280i
$283$			26.5449i			1.57793i	0.614436	+	0.788966i	$0.289383\pi$
$283$			26.5449i			1.57793i	−0.614436	+	0.788966i	$0.710617\pi$
$284$			9.56280i			0.567448i
$285$	−13.3310	−	5.29686i	−0.789662	−	0.313759i
$286$	3.95023	+	14.2918i	0.233582	+	0.845093i
$287$		−	2.83876i		−	0.167567i
$288$	−12.4512	−	11.7495i	−0.733695	−	0.692346i
$289$	−16.9770			−0.998649
$290$		−	13.6340i		−	0.800616i
$291$	−8.14602	−	3.23669i	−0.477528	−	0.189738i
$292$		−	4.40952i		−	0.258048i
$293$	−32.2722			−1.88536			−0.942682	−	0.333694i	$-0.891705\pi$
$293$	−32.2722			−1.88536			−0.942682	+	0.333694i	$0.891705\pi$
$294$	1.38183	+	0.549047i	0.0805899	+	0.0320211i
$295$	−5.43378			−0.316367
$296$	21.5742			1.25397
$297$	−11.1791	−	13.1159i	−0.648678	−	0.761063i
$298$	6.72904			0.389803
$299$	29.9954			1.73468
$300$	2.00964	+	0.798497i	0.116027	+	0.0461013i
$301$	−9.44759			−0.544550
$302$			7.05342i			0.405879i
$303$	4.78378	+	1.90075i	0.274821	+	0.109195i
$304$			0.410569i			0.0235477i
$305$	27.3082			1.56366
$306$	−0.283912	−	0.267912i	−0.0162302	−	0.0153155i
$307$			1.71093i			0.0976479i	0.998807	+	0.0488240i	$0.0155473\pi$
$307$			1.71093i			0.0976479i	−0.998807	+	0.0488240i	$0.984453\pi$
$308$	−1.11599	−	4.03761i	−0.0635893	−	0.230064i
$309$	3.39170	+	1.34763i	0.192947	+	0.0766642i
$310$			11.4744i			0.651700i
$311$		−	7.97842i		−	0.452415i	−0.974079	−	0.226207i	$-0.927367\pi$
$311$		−	7.97842i		−	0.452415i	0.974079	−	0.226207i	$-0.0726327\pi$
$312$	−9.33004	+	23.4816i	−0.528210	+	1.32939i
$313$	7.94955			0.449335			0.224668	−	0.974435i	$-0.427870\pi$
$313$	7.94955			0.449335			0.224668	+	0.974435i	$0.427870\pi$
$314$	−8.10437			−0.457356
$315$	5.33944	+	5.03853i	0.300844	+	0.283889i
$316$		−	14.6905i		−	0.826406i
$317$			9.99277i			0.561250i	0.959817	+	0.280625i	$0.0905417\pi$
$317$			9.99277i			0.561250i	−0.959817	+	0.280625i	$0.909458\pi$
$318$	−6.22708	+	15.6722i	−0.349197	+	0.878853i
$319$	−20.7468	+	5.73436i	−1.16160	+	0.321063i
$320$			11.3946i			0.636975i
$321$	−25.0632	−	9.95844i	−1.39889	−	0.555826i
$322$	4.94454			0.275549
$323$			0.512977i			0.0285428i
$324$	−0.658648	−	11.3482i	−0.0365915	−	0.630455i
$325$		−	5.14786i		−	0.285552i
$326$	6.98365			0.386788
$327$	2.68358	−	6.75399i	0.148403	−	0.373496i
$328$	7.95197			0.439074
$329$	−0.242178			−0.0133517
$330$	−1.30731	+	11.9971i	−0.0719648	+	0.660419i
$331$	33.5249			1.84270			0.921348	−	0.388738i	$-0.127089\pi$
$331$	33.5249			1.84270			0.921348	+	0.388738i	$0.127089\pi$
$332$	−19.7880			−1.08601
$333$	16.8045	+	15.8574i	0.920881	+	0.868983i
$334$	−2.27264			−0.124353
$335$		−	4.75247i		−	0.259655i
$336$	0.0775883	−	0.195273i	0.00423279	−	0.0106530i
$337$		−	12.1898i		−	0.664019i	−0.943276	−	0.332009i	$-0.892273\pi$
$337$		−	12.1898i		−	0.664019i	0.943276	−	0.332009i	$-0.107727\pi$
$338$	12.1224			0.659374
$339$	−12.0011	+	30.2041i	−0.651810	+	1.64046i
$340$		−	0.468485i		−	0.0254072i
$341$	17.4605	−	4.82603i	0.945537	−	0.261344i
$342$	5.98197	−	6.33923i	0.323468	−	0.342786i
$343$			1.00000i			0.0539949i
$344$		−	26.4647i		−	1.42688i
$345$	22.6877	+	9.01458i	1.22147	+	0.485329i
$346$	2.60251			0.139912
$347$	−2.32869			−0.125011			−0.0625054	−	0.998045i	$-0.519909\pi$
$347$	−2.32869			−0.125011			−0.0625054	+	0.998045i	$0.519909\pi$
$348$	−13.1942	−	5.24251i	−0.707285	−	0.281028i
$349$			18.9275i			1.01317i	0.862191	+	0.506584i	$0.169092\pi$
$349$			18.9275i			1.01317i	−0.862191	+	0.506584i	$0.830908\pi$
$350$		−	0.848591i		−	0.0453591i
$351$	−24.5268	+	11.4325i	−1.30915	+	0.610222i
$352$	18.2425	−	5.04220i	0.972330	−	0.268750i
$353$			21.8920i			1.16519i	0.812761	+	0.582597i	$0.197964\pi$
$353$			21.8920i			1.16519i	−0.812761	+	0.582597i	$0.802036\pi$
$354$	1.21914	−	3.06830i	0.0647965	−	0.163078i
$355$	18.5280			0.983366
$356$			3.26163i			0.172866i
$357$	0.0969411	−	0.243979i	0.00513066	−	0.0129127i
$358$			8.41271i			0.444626i
$359$	−27.6170			−1.45757			−0.728786	−	0.684742i	$-0.759915\pi$
$359$	−27.6170			−1.45757			−0.728786	+	0.684742i	$0.759915\pi$
$360$	−14.1140	+	14.9569i	−0.743872	+	0.788298i
$361$	7.54620			0.397168
$362$	6.89403			0.362342
$363$	18.8058	−	3.05658i	0.987047	−	0.160429i
$364$	−6.57760			−0.344760
$365$	−8.54350			−0.447187
$366$	−6.12694	+	15.4202i	−0.320260	+	0.806025i
$367$	21.0812			1.10043			0.550214	−	0.835024i	$-0.314546\pi$
$367$	21.0812			1.10043			0.550214	+	0.835024i	$0.314546\pi$
$368$		−	0.698736i		−	0.0364241i
$369$	6.19393	+	5.84486i	0.322443	+	0.304271i
$370$		−	16.1797i		−	0.841144i
$371$	−11.3416			−0.588828
$372$	11.1043	+	4.41209i	0.575729	+	0.228756i
$373$		−	31.1830i		−	1.61459i	−0.590145	−	0.807297i	$-0.700929\pi$
$373$		−	31.1830i		−	1.61459i	0.590145	−	0.807297i	$-0.299071\pi$
$374$	0.415966	−	0.114972i	0.0215091	−	0.00594506i
$375$	−6.27843	+	15.8014i	−0.324217	+	0.815982i
$376$		−	0.678390i		−	0.0349853i
$377$			33.7981i			1.74069i
$378$	−4.04308	+	1.88457i	−0.207954	+	0.0969319i
$379$	−11.2956			−0.580219			−0.290109	−	0.956994i	$-0.593692\pi$
$379$	−11.2956			−0.580219			−0.290109	+	0.956994i	$0.593692\pi$
$380$	10.4604			0.536607
$381$	−0.0695216	+	0.174971i	−0.00356170	+	0.00896402i
$382$			16.4413i			0.841210i
$383$			2.15474i			0.110102i	0.998484	+	0.0550511i	$0.0175322\pi$
$383$			2.15474i			0.110102i	−0.998484	+	0.0550511i	$0.982468\pi$
$384$	11.9369	+	4.74293i	0.609153	+	0.242037i
$385$	−7.82293	+	2.16224i	−0.398693	+	0.110198i
$386$		−	0.352118i		−	0.0179223i
$387$	19.4521	−	20.6138i	0.988805	−	1.04786i
$388$	6.39190			0.324500
$389$		−	10.8798i		−	0.551626i	−0.961211	−	0.275813i	$-0.911053\pi$
$389$		−	10.8798i		−	0.551626i	0.961211	−	0.275813i	$-0.0889471\pi$
$390$	17.6103	+	6.99715i	0.891731	+	0.354314i
$391$		−	0.873021i		−	0.0441506i
$392$	−2.80121			−0.141482
$393$	20.6468	+	8.20365i	1.04149	+	0.413820i
$394$	−12.5669			−0.633110
$395$	−28.4630			−1.43213
$396$	11.1075	+	5.87824i	0.558172	+	0.295393i
$397$	−33.3972			−1.67616			−0.838079	−	0.545549i	$-0.816321\pi$
$397$	−33.3972			−1.67616			−0.838079	+	0.545549i	$0.816321\pi$
$398$	22.0973			1.10764
$399$	5.44759	+	2.16451i	0.272721	+	0.108361i
$400$	−0.119918			−0.00599592
$401$		−	2.29520i		−	0.114617i	−0.998357	−	0.0573085i	$-0.981748\pi$
$401$		−	2.29520i		−	0.114617i	0.998357	−	0.0573085i	$-0.0182518\pi$
$402$	2.68358	+	1.06628i	0.133845	+	0.0531811i
$403$		−	28.4445i		−	1.41692i
$404$	−3.75366			−0.186752
$405$	−21.9873	+	1.27614i	−1.09256	+	0.0634118i
$406$			5.57140i			0.276504i
$407$	−24.6206	+	6.80508i	−1.22040	+	0.337315i
$408$	0.683437	+	0.271552i	0.0338352	+	0.0134438i
$409$		−	0.487637i		−	0.0241121i	−0.999927	−	0.0120561i	$-0.996162\pi$
$409$		−	0.487637i		−	0.0241121i	0.999927	−	0.0120561i	$-0.00383765\pi$
$410$		−	5.96365i		−	0.294524i
$411$	−11.3149	+	28.4770i	−0.558121	+	1.40467i
$412$	−2.66135			−0.131115
$413$	2.22046			0.109262
$414$	−10.1805	+	10.7886i	−0.500347	+	0.530229i
$415$			38.3395i			1.88201i
$416$		−	29.7186i		−	1.45707i
$417$	−1.40461	+	3.53508i	−0.0687838	+	0.173114i
$418$	2.56711	+	9.28773i	0.125561	+	0.454278i
$419$		−	16.5555i		−	0.808788i	−0.914585	−	0.404394i	$-0.867483\pi$
$419$		−	16.5555i		−	0.808788i	0.914585	−	0.404394i	$-0.132517\pi$
$420$	−4.97512	−	1.97678i	−0.242761	−	0.0964569i
$421$	−1.95797			−0.0954255			−0.0477127	−	0.998861i	$-0.515193\pi$
$421$	−1.95797			−0.0954255			−0.0477127	+	0.998861i	$0.515193\pi$
$422$		−	13.2431i		−	0.644666i
$423$	0.498631	−	0.528410i	0.0242442	−	0.0256922i
$424$		−	31.7703i		−	1.54290i
$425$	−0.149829			−0.00726779
$426$	−4.15700	+	10.4622i	−0.201407	+	0.506897i
$427$	−11.1592			−0.540033
$428$	19.6662			0.950603
$429$	3.24076	−	29.7404i	0.156465	−	1.43588i
$430$	−19.8474			−0.957128
$431$	15.3532			0.739536			0.369768	−	0.929124i	$-0.379437\pi$
$431$	15.3532			0.739536			0.369768	+	0.929124i	$0.379437\pi$
$432$	0.266318	+	0.571347i	0.0128132	+	0.0274889i
$433$	9.06597			0.435683			0.217841	−	0.975984i	$-0.430098\pi$
$433$	9.06597			0.435683			0.217841	+	0.975984i	$0.430098\pi$
$434$		−	4.68888i		−	0.225074i
$435$	−10.1574	+	25.5640i	−0.487011	+	1.22570i
$436$			5.29962i			0.253806i
$437$	19.4929			0.932472
$438$	1.91684	−	4.82427i	0.0915903	−	0.230512i
$439$		−	3.83456i		−	0.183014i	−0.995804	−	0.0915069i	$-0.970832\pi$
$439$		−	3.83456i		−	0.183014i	0.995804	−	0.0915069i	$-0.0291683\pi$
$440$	−6.05689	−	21.9137i	−0.288751	−	1.04469i
$441$	−2.18191	−	2.05895i	−0.103901	−	0.0980451i
$442$		−	0.677642i		−	0.0322321i
$443$			7.53453i			0.357976i	0.983851	+	0.178988i	$0.0572824\pi$
$443$			7.53453i			0.357976i	−0.983851	+	0.178988i	$0.942718\pi$
$444$	−15.6579	−	6.22139i	−0.743090	−	0.295254i
$445$	6.31945			0.299571
$446$	15.4373			0.730976
$447$	−12.6171	−	5.01319i	−0.596768	−	0.237116i
$448$		−	4.65628i		−	0.219988i
$449$		−	11.0420i		−	0.521102i	−0.965460	−	0.260551i	$-0.916096\pi$
$449$		−	11.0420i		−	0.521102i	0.965460	−	0.260551i	$-0.0839042\pi$
$450$	1.85155	+	1.74720i	0.0872830	+	0.0823640i
$451$	−9.07485	+	2.50827i	−0.427318	+	0.118110i
$452$		−	23.7001i		−	1.11476i
$453$	5.25485	−	13.2253i	0.246895	−	0.621379i
$454$	−11.4092			−0.535462
$455$			12.7442i			0.597456i
$456$	−6.06325	+	15.2599i	−0.283938	+	0.714608i
$457$			6.31005i			0.295172i	0.989049	+	0.147586i	$0.0471503\pi$
$457$			6.31005i			0.295172i	−0.989049	+	0.147586i	$0.952850\pi$
$458$	−16.5857			−0.775001
$459$	0.332745	+	0.713857i	0.0155312	+	0.0333200i
$460$	−17.8023			−0.830034
$461$	3.42269			0.159411			0.0797053	−	0.996818i	$-0.474602\pi$
$461$	3.42269			0.159411			0.0797053	+	0.996818i	$0.474602\pi$
$462$	0.534218	−	4.90250i	0.0248541	−	0.228085i
$463$	4.98281			0.231571			0.115785	−	0.993274i	$-0.463062\pi$
$463$	4.98281			0.231571			0.115785	+	0.993274i	$0.463062\pi$
$464$	0.787320			0.0365504
$465$	8.54848	−	21.5146i	0.396426	−	0.997717i
$466$	3.81105			0.176543
$467$			1.41768i			0.0656026i	0.999462	+	0.0328013i	$0.0104429\pi$
$467$			1.41768i			0.0656026i	−0.999462	+	0.0328013i	$0.989557\pi$
$468$	13.5429	−	14.3517i	0.626022	−	0.663409i
$469$			1.94205i			0.0896757i
$470$	−0.508765			−0.0234676
$471$	15.1958	+	6.03782i	0.700188	+	0.278208i
$472$			6.21998i			0.286298i
$473$	8.34769	+	30.2017i	0.383827	+	1.38868i
$474$	6.38604	−	16.0723i	0.293321	−	0.738223i
$475$		−	3.34541i		−	0.153498i
$476$			0.191442i			0.00877473i
$477$	23.3518	−	24.7464i	1.06921	−	1.13306i
$478$	−1.19775			−0.0547840
$479$	23.8833			1.09126			0.545628	−	0.838028i	$-0.316291\pi$
$479$	23.8833			1.09126			0.545628	+	0.838028i	$0.316291\pi$
$480$	8.93138	−	22.4783i	0.407660	−	1.02599i
$481$			40.1089i			1.82881i
$482$			13.2190i			0.602108i
$483$	−9.27111	−	3.68372i	−0.421850	−	0.167615i
$484$	−11.9212	+	7.13509i	−0.541874	+	0.324322i
$485$		−	12.3844i		−	0.562346i
$486$	4.21252	−	12.7019i	0.191084	−	0.576169i
$487$	24.6191			1.11560			0.557799	−	0.829976i	$-0.311646\pi$
$487$	24.6191			1.11560			0.557799	+	0.829976i	$0.311646\pi$
$488$		−	31.2594i		−	1.41505i
$489$	−13.0945	−	5.20287i	−0.592152	−	0.235282i
$490$			2.10079i			0.0949041i
$491$	−4.71511			−0.212790			−0.106395	−	0.994324i	$-0.533931\pi$
$491$	−4.71511			−0.212790			−0.106395	+	0.994324i	$0.533931\pi$
$492$	−5.77130	−	2.29313i	−0.260190	−	0.103382i
$493$	0.983700			0.0443036
$494$	15.1305			0.680751
$495$	11.3892	−	21.5209i	0.511905	−	0.967291i
$496$	−0.662608			−0.0297520
$497$	−7.57130			−0.339619
$498$	−21.6492	−	8.60194i	−0.970123	−	0.385462i
$499$	13.8960			0.622070			0.311035	−	0.950399i	$-0.399324\pi$
$499$	13.8960			0.622070			0.311035	+	0.950399i	$0.399324\pi$
$500$		−	12.3988i		−	0.554492i
$501$	4.26124	+	1.69313i	0.190378	+	0.0756436i
$502$			17.9315i			0.800321i
$503$	21.4181			0.954987			0.477494	−	0.878635i	$-0.341545\pi$
$503$	21.4181			0.954987			0.477494	+	0.878635i	$0.341545\pi$
$504$	5.76754	−	6.11199i	0.256907	−	0.272250i
$505$			7.27277i			0.323634i
$506$	−4.36889	−	15.8065i	−0.194221	−	0.702686i
$507$	−22.7298	−	9.03131i	−1.00947	−	0.401095i
$508$		−	0.137293i		−	0.00609141i
$509$		−	1.52865i		−	0.0677564i	−0.999426	−	0.0338782i	$-0.989214\pi$
$509$		−	1.52865i		−	0.0677564i	0.999426	−	0.0338782i	$-0.0107858\pi$
$510$	0.203653	−	0.512550i	0.00901791	−	0.0226961i
$511$	3.49122			0.154442
$512$	−1.37194			−0.0606317
$513$	−15.9391	+	7.42956i	−0.703727	+	0.328023i
$514$		−	6.31501i		−	0.278543i
$515$			5.15639i			0.227218i
$516$	−7.63169	+	19.2073i	−0.335966	+	0.845553i
$517$	0.213983	+	0.774184i	0.00941095	+	0.0340486i
$518$			6.61169i			0.290501i
$519$	−4.87975	−	1.93889i	−0.214197	−	0.0851077i
$520$	−35.6991			−1.56551
$521$			14.5996i			0.639621i	0.947481	+	0.319811i	$0.103619\pi$
$521$			14.5996i			0.639621i	−0.947481	+	0.319811i	$0.896381\pi$
$522$	−12.1563	−	11.4712i	−0.532067	−	0.502081i
$523$			7.63979i			0.334065i	0.985951	+	0.167032i	$0.0534184\pi$
$523$			7.63979i			0.334065i	−0.985951	+	0.167032i	$0.946582\pi$
$524$	−16.2008			−0.707736
$525$	−0.632207	+	1.59112i	−0.0275918	+	0.0694424i
$526$	−0.852713			−0.0371801
$527$	−0.827881			−0.0360631
$528$	−0.692796	−	0.0754928i	−0.0301501	−	0.00328540i
$529$	−10.1744			−0.442367
$530$	−23.8264			−1.03495
$531$	−4.57181	+	4.84486i	−0.198400	+	0.210249i
$532$	−4.27454			−0.185325
$533$			14.7837i			0.640351i
$534$	−1.41785	+	3.56841i	−0.0613563	+	0.154420i
$535$		−	38.1035i		−	1.64736i
$536$	−5.44010			−0.234976
$537$	6.26753	−	15.7740i	0.270464	−	0.680698i
$538$			11.9726i			0.516177i
$539$	3.19676	−	0.883578i	0.137694	−	0.0380584i
$540$	14.5567	−	6.78518i	0.626419	−	0.291988i
$541$		−	23.4249i		−	1.00711i	−0.863962	−	0.503557i	$-0.832025\pi$
$541$		−	23.4249i		−	1.00711i	0.863962	−	0.503557i	$-0.167975\pi$
$542$			26.7133i			1.14744i
$543$	−12.9264	−	5.13611i	−0.554727	−	0.220411i
$544$	−0.864963			−0.0370850
$545$	10.2681			0.439836
$546$	−7.19627	−	2.85932i	−0.307972	−	0.122367i
$547$			14.5891i			0.623785i	0.950117	+	0.311893i	$0.100963\pi$
$547$			14.5891i			0.623785i	−0.950117	+	0.311893i	$0.899037\pi$
$548$		−	22.3449i		−	0.954528i
$549$	22.9763	−	24.3485i	0.980603	−	1.03917i
$550$	−2.71274	+	0.749797i	−0.115672	+	0.0319714i
$551$			21.9642i			0.935705i
$552$	10.3189	−	25.9703i	0.439201	−	1.10537i
$553$	11.6311			0.494607
$554$			7.43243i			0.315774i
$555$	−12.0540	+	30.3373i	−0.511665	+	1.28775i
$556$		−	2.77385i		−	0.117638i
$557$	−1.76892			−0.0749516			−0.0374758	−	0.999298i	$-0.511932\pi$
$557$	−1.76892			−0.0749516			−0.0374758	+	0.999298i	$0.511932\pi$
$558$	10.2307	+	9.65416i	0.433101	+	0.408693i
$559$	49.2010			2.08098
$560$	0.296873			0.0125452
$561$	−0.865599	−	0.0943228i	−0.0365456	−	0.00398231i
$562$	22.6231			0.954296
$563$	−34.9625			−1.47349			−0.736747	−	0.676168i	$-0.763639\pi$
$563$	−34.9625			−1.47349			−0.736747	+	0.676168i	$0.763639\pi$
$564$	−0.195629	+	0.492355i	−0.00823747	+	0.0207319i
$565$	−45.9193			−1.93184
$566$		−	22.7880i		−	0.957851i
$567$	8.98488	−	0.521482i	0.377329	−	0.0219002i
$568$		−	21.2088i		−	0.889902i
$569$	−27.1063			−1.13636			−0.568178	−	0.822906i	$-0.692351\pi$
$569$	−27.1063			−1.13636			−0.568178	+	0.822906i	$0.692351\pi$
$570$	11.4443	+	4.54719i	0.479348	+	0.190461i
$571$		−	7.51053i		−	0.314306i	−0.987574	−	0.157153i	$-0.949768\pi$
$571$		−	7.51053i		−	0.314306i	0.987574	−	0.157153i	$-0.0502316\pi$
$572$	5.81182	+	21.0270i	0.243005	+	0.879184i
$573$	12.2489	−	30.8278i	0.511705	−	1.28785i
$574$			2.43699i			0.101718i
$575$			5.69346i			0.237434i
$576$	10.1596	+	9.58702i	0.423316	+	0.399459i
$577$	38.1511			1.58825			0.794126	−	0.607753i	$-0.207929\pi$
$577$	38.1511			1.58825			0.794126	+	0.607753i	$0.207929\pi$
$578$	14.5742			0.606208
$579$	−0.262330	+	0.660227i	−0.0109021	+	0.0274381i
$580$		−	20.0592i		−	0.832912i
$581$		−	15.6670i		−	0.649979i
$582$	6.99310	+	2.77859i	0.289873	+	0.115176i
$583$	10.0212	+	36.2565i	0.415036	+	1.50159i
$584$			9.77964i			0.404684i
$585$	−27.8067	−	26.2396i	−1.14966	−	1.08487i
$586$	27.7047			1.14447
$587$			21.8338i			0.901177i	0.892732	+	0.450589i	$0.148786\pi$
$587$			21.8338i			0.901177i	−0.892732	+	0.450589i	$0.851214\pi$
$588$	2.03303	+	0.807792i	0.0838409	+	0.0333128i
$589$		−	18.4850i		−	0.761662i
$590$	4.66473			0.192044
$591$	23.5631	+	9.36241i	0.969258	+	0.385118i
$592$	0.934329			0.0384007
$593$	−41.3070			−1.69627			−0.848137	−	0.529777i	$-0.822276\pi$
$593$	−41.3070			−1.69627			−0.848137	+	0.529777i	$0.822276\pi$
$594$	9.59691	+	11.2596i	0.393766	+	0.461987i
$595$	0.370921			0.0152063
$596$	9.90019			0.405528
$597$	−41.4328	−	16.4626i	−1.69573	−	0.673770i
$598$	−25.7501			−1.05300
$599$			19.0163i			0.776986i	0.921452	+	0.388493i	$0.127004\pi$
$599$			19.0163i			0.776986i	−0.921452	+	0.388493i	$0.872996\pi$
$600$	−4.45707	−	1.77094i	−0.181959	−	0.0722985i
$601$			27.9294i			1.13927i	0.821899	+	0.569633i	$0.192914\pi$
$601$			27.9294i			1.13927i	−0.821899	+	0.569633i	$0.807086\pi$
$602$	8.11046			0.330558
$603$	−4.23739	−	3.99858i	−0.172560	−	0.162835i
$604$			10.3774i			0.422252i
$605$	13.8243	+	23.0975i	0.562039	+	0.939048i
$606$	−4.10672	−	1.63174i	−0.166824	−	0.0662848i
$607$		−	45.3889i		−	1.84228i	−0.389231	−	0.921140i	$-0.627259\pi$
$607$		−	45.3889i		−	1.84228i	0.389231	−	0.921140i	$-0.372741\pi$
$608$		−	19.3130i		−	0.783245i
$609$	4.15073	−	10.4465i	0.168196	−	0.423313i
$610$	−23.4432			−0.949189
$611$	1.26121			0.0510230
$612$	−0.417710	−	0.394169i	−0.0168849	−	0.0159333i
$613$			21.9987i			0.888521i	0.895898	+	0.444260i	$0.146533\pi$
$613$			21.9987i			0.888521i	−0.895898	+	0.444260i	$0.853467\pi$
$614$		−	1.46878i		−	0.0592751i
$615$	−4.44296	+	11.1820i	−0.179158	+	0.450900i
$616$	2.47509	+	8.95480i	0.0997241	+	0.360799i
$617$		−	9.86433i		−	0.397123i	−0.980088	−	0.198562i	$-0.936373\pi$
$617$		−	9.86433i		−	0.397123i	0.980088	−	0.198562i	$-0.0636270\pi$
$618$	−2.91167	−	1.15690i	−0.117124	−	0.0465374i
$619$	28.5296			1.14670			0.573351	−	0.819310i	$-0.305643\pi$
$619$	28.5296			1.14670			0.573351	+	0.819310i	$0.305643\pi$
$620$			16.8818i			0.677989i
$621$	27.1263	−	12.6442i	1.08854	−	0.507393i
$622$			6.84922i			0.274629i
$623$	−2.58238			−0.103461
$624$	−0.404063	+	1.01694i	−0.0161755	+	0.0407101i
$625$	−28.9654			−1.15861
$626$	−6.82444			−0.272760
$627$	2.10605	−	19.3272i	0.0841075	−	0.771853i
$628$	−11.9237			−0.475806
$629$	1.16738			0.0465464
$630$	−4.58374	−	4.32542i	−0.182621	−	0.172329i
$631$	4.84996			0.193074			0.0965369	−	0.995329i	$-0.469223\pi$
$631$	4.84996			0.193074			0.0965369	+	0.995329i	$0.469223\pi$
$632$			32.5813i			1.29601i
$633$	−9.86624	+	24.8311i	−0.392148	+	0.986949i
$634$		−	8.57848i		−	0.340695i
$635$	−0.266007			−0.0105562
$636$	−9.16167	+	23.0579i	−0.363284	+	0.914305i
$637$		−	5.20778i		−	0.206340i
$638$	17.8104	−	4.92277i	0.705122	−	0.194894i
$639$	15.5889	−	16.5199i	0.616687	−	0.653518i
$640$			18.1477i			0.717349i
$641$		−	31.4366i		−	1.24167i	−0.783940	−	0.620836i	$-0.786793\pi$
$641$		−	31.4366i		−	1.24167i	0.783940	−	0.620836i	$-0.213207\pi$
$642$	21.5160	+	8.54901i	0.849167	+	0.337402i
$643$	−17.5992			−0.694045			−0.347023	−	0.937857i	$-0.612807\pi$
$643$	−17.5992			−0.694045			−0.347023	+	0.937857i	$0.612807\pi$
$644$	7.27472			0.286664
$645$	37.2143	+	14.7865i	1.46531	+	0.582217i
$646$		−	0.440374i		−	0.0173263i
$647$		−	5.27548i		−	0.207400i	−0.994609	−	0.103700i	$-0.966932\pi$
$647$		−	5.27548i		−	0.207400i	0.994609	−	0.103700i	$-0.0330682\pi$
$648$	1.46078	+	25.1685i	0.0573848	+	0.988713i
$649$	−1.96195	−	7.09829i	−0.0770134	−	0.278632i
$650$			4.41928i			0.173338i
$651$	−3.49325	+	8.79175i	−0.136911	+	0.344576i
$652$	10.2748			0.402391
$653$			20.2731i			0.793348i	0.917959	+	0.396674i	$0.129836\pi$
$653$			20.2731i			0.793348i	−0.917959	+	0.396674i	$0.870164\pi$
$654$	−2.30377	+	5.79809i	−0.0900846	+	0.226723i
$655$			31.3893i			1.22648i
$656$	0.344382			0.0134459
$657$	−7.18823	+	7.61753i	−0.280440	+	0.297188i
$658$	0.207902			0.00810485
$659$	−4.30970			−0.167882			−0.0839410	−	0.996471i	$-0.526751\pi$
$659$	−4.30970			−0.167882			−0.0839410	+	0.996471i	$0.526751\pi$
$660$	−1.92339	+	17.6509i	−0.0748678	+	0.687060i
$661$	−15.5035			−0.603018			−0.301509	−	0.953463i	$-0.597490\pi$
$661$	−15.5035			−0.603018			−0.301509	+	0.953463i	$0.597490\pi$
$662$	−28.7801			−1.11857
$663$	−0.504848	+	1.27059i	−0.0196067	+	0.0493457i
$664$	43.8867			1.70313
$665$			8.28197i			0.321161i
$666$	−14.4261	−	13.6131i	−0.559001	−	0.527497i
$667$		−	37.3802i		−	1.44737i
$668$	−3.34365			−0.129370
$669$	−28.9452	−	11.5009i	−1.11909	−	0.444650i
$670$			4.07985i			0.157618i
$671$	9.86006	+	35.6734i	0.380643	+	1.37716i
$672$	−3.64972	+	9.18554i	−0.140791	+	0.354340i
$673$		−	43.5361i		−	1.67819i	−0.543982	−	0.839097i	$-0.683084\pi$
$673$		−	43.5361i		−	1.67819i	0.543982	−	0.839097i	$-0.316916\pi$
$674$			10.4645i			0.403079i
$675$	−2.17001	−	4.65546i	−0.0835239	−	0.179189i
$676$	17.8353			0.685973
$677$	−45.1287			−1.73444			−0.867219	−	0.497928i	$-0.834094\pi$
$677$	−45.1287			−1.73444			−0.867219	+	0.497928i	$0.834094\pi$
$678$	10.3026	−	25.9293i	0.395668	−	0.995808i
$679$			5.06076i			0.194214i
$680$			1.03903i			0.0398449i
$681$	21.3925	+	8.49996i	0.819763	+	0.325719i
$682$	−14.9892	+	4.14300i	−0.573968	+	0.158644i
$683$			15.5761i			0.596004i	0.954565	+	0.298002i	$0.0963202\pi$
$683$			15.5761i			0.596004i	−0.954565	+	0.298002i	$0.903680\pi$
$684$	8.80104	−	9.32667i	0.336516	−	0.356614i
$685$	−43.2936			−1.65416
$686$		−	0.858468i		−	0.0327765i
$687$	31.0986	+	12.3565i	1.18649	+	0.471430i
$688$		−	1.14613i		−	0.0436957i
$689$	59.0647			2.25019
$690$	−19.4767	−	7.73873i	−0.741465	−	0.294609i
$691$	4.54246			0.172803			0.0864016	−	0.996260i	$-0.472463\pi$
$691$	4.54246			0.172803			0.0864016	+	0.996260i	$0.472463\pi$
$692$	3.82897			0.145556
$693$	−4.65407	+	8.79429i	−0.176794	+	0.334068i
$694$	1.99911			0.0758851
$695$	−5.37438			−0.203862
$696$	29.2628	+	11.6271i	1.10920	+	0.440723i
$697$	0.430281			0.0162980
$698$		−	16.2487i		−	0.615022i
$699$	−7.14579	−	2.83926i	−0.270279	−	0.107391i
$700$		−	1.24850i		−	0.0471889i
$701$	35.4949			1.34062			0.670312	−	0.742080i	$-0.266160\pi$
$701$	35.4949			1.34062			0.670312	+	0.742080i	$0.266160\pi$
$702$	21.0555	−	9.81444i	0.794689	−	0.370422i
$703$			26.0653i			0.983072i
$704$	−14.8850	+	4.11418i	−0.561000	+	0.155059i
$705$	0.953944	+	0.379034i	0.0359276	+	0.0142752i
$706$		−	18.7936i		−	0.707307i
$707$		−	2.97195i		−	0.111772i
$708$	1.79367	−	4.51427i	0.0674103	−	0.169657i
$709$	−39.3543			−1.47798			−0.738990	−	0.673716i	$-0.764697\pi$
$709$	−39.3543			−1.47798			−0.738990	+	0.673716i	$0.764697\pi$
$710$	−15.9057			−0.596932
$711$	−23.9479	+	25.3781i	−0.898117	+	0.951755i
$712$		−	7.23379i		−	0.271098i
$713$			31.4591i			1.17815i
$714$	−0.0832208	+	0.209448i	−0.00311446	+	0.00783841i
$715$	40.7401	−	11.2605i	1.52359	−	0.421118i
$716$			12.3773i			0.462562i
$717$	2.24581	+	0.892336i	0.0838714	+	0.0333249i
$718$	23.7083			0.884788
$719$			24.1882i			0.902068i	0.892507	+	0.451034i	$0.148945\pi$
$719$			24.1882i			0.902068i	−0.892507	+	0.451034i	$0.851055\pi$
$720$	−0.611245	+	0.647750i	−0.0227798	+	0.0241402i
$721$		−	2.10711i		−	0.0784729i
$722$	−6.47817			−0.241093
$723$	9.84824	−	24.7859i	0.366260	−	0.921796i
$724$	10.1429			0.376959
$725$	−6.41526			−0.238257
$726$	−16.1442	+	2.62398i	−0.599166	+	0.0973850i
$727$	−27.5666			−1.02239			−0.511195	−	0.859465i	$-0.670797\pi$
$727$	−27.5666			−1.02239			−0.511195	+	0.859465i	$0.670797\pi$
$728$	14.5881			0.540671
$729$	−17.3616	+	20.6779i	−0.643021	+	0.765849i
$730$	7.33433			0.271456
$731$		−	1.43200i		−	0.0529646i
$732$	−9.01434	+	22.6871i	−0.333180	+	0.838539i
$733$			20.8387i			0.769695i	0.922980	+	0.384848i	$0.125746\pi$
$733$			20.8387i			0.769695i	−0.922980	+	0.384848i	$0.874254\pi$
$734$	−18.0975			−0.667991
$735$	1.56511	−	3.93903i	0.0577298	−	0.145293i
$736$			32.8682i			1.21154i
$737$	6.20828	−	1.71596i	0.228685	−	0.0632080i
$738$	−5.31729	−	5.01762i	−0.195732	−	0.184701i
$739$			39.4845i			1.45246i	0.687452	+	0.726230i	$0.258729\pi$
$739$			39.4845i			1.45246i	−0.687452	+	0.726230i	$0.741271\pi$
$740$		−	23.8046i		−	0.875076i
$741$	−28.3699	−	11.2723i	−1.04219	−	0.414098i
$742$	9.73643			0.357436
$743$	−18.3829			−0.674405			−0.337202	−	0.941432i	$-0.609481\pi$
$743$	−18.3829			−0.674405			−0.337202	+	0.941432i	$0.609481\pi$
$744$	−24.6275	−	9.78534i	−0.902889	−	0.358748i
$745$		−	19.1817i		−	0.702764i
$746$			26.7696i			0.980105i
$747$	34.1841	+	32.2576i	1.25073	+	1.18024i
$748$	0.611994	−	0.169154i	0.0223767	−	0.00618488i
$749$			15.5706i			0.568939i
$750$	5.38984	−	13.5650i	0.196809	−	0.495325i
$751$	−45.7526			−1.66954			−0.834768	−	0.550601i	$-0.814399\pi$
$751$	−45.7526			−1.66954			−0.834768	+	0.550601i	$0.814399\pi$
$752$		−	0.0293796i		−	0.00107136i
$753$	13.3591	−	33.6218i	0.486832	−	1.22525i
$754$		−	29.0146i		−	1.05665i
$755$	20.1064			0.731747
$756$	−5.94844	+	2.77270i	−0.216343	+	0.100842i
$757$	−25.8349			−0.938986			−0.469493	−	0.882936i	$-0.655563\pi$
$757$	−25.8349			−0.938986			−0.469493	+	0.882936i	$0.655563\pi$
$758$	9.69696			0.352209
$759$	−3.58423	+	32.8924i	−0.130099	+	1.19392i
$760$	−23.1995			−0.841536
$761$	−33.4984			−1.21432			−0.607158	−	0.794581i	$-0.707690\pi$
$761$	−33.4984			−1.21432			−0.607158	+	0.794581i	$0.707690\pi$
$762$	0.0596821	−	0.150207i	0.00216206	−	0.00544142i
$763$	−4.19595			−0.151904
$764$			24.1895i			0.875144i
$765$	−0.763707	+	0.809317i	−0.0276119	+	0.0292609i
$766$		−	1.84978i		−	0.0668352i
$767$	−11.5637			−0.417541
$768$	−25.2374	−	10.0276i	−0.910675	−	0.361841i
$769$		−	35.1763i		−	1.26849i	−0.773132	−	0.634245i	$-0.781311\pi$
$769$		−	35.1763i		−	1.26849i	0.773132	−	0.634245i	$-0.218689\pi$
$770$	6.71573	−	1.85621i	0.242018	−	0.0668933i
$771$	−4.70473	+	11.8408i	−0.169437	+	0.426435i
$772$		−	0.518057i		−	0.0186453i
$773$		−	41.0079i		−	1.47495i	−0.675374	−	0.737475i	$-0.736018\pi$
$773$		−	41.0079i		−	1.47495i	0.675374	−	0.737475i	$-0.263982\pi$
$774$	−16.6990	+	17.6963i	−0.600233	+	0.636081i
$775$	5.39907			0.193940
$776$	−14.1762			−0.508898
$777$	4.92576	−	12.3970i	0.176711	−	0.444742i
$778$			9.33994i			0.334853i
$779$			9.60735i			0.344219i
$780$	25.9093	+	10.2946i	0.927703	+	0.368607i
$781$	6.68984	+	24.2037i	0.239381	+	0.866075i
$782$			0.749461i			0.0268007i
$783$	14.2472	+	30.5653i	0.509152	+	1.09231i
$784$	−0.121314			−0.00433265
$785$			23.1022i			0.824554i
$786$	−17.7246	−	7.04258i	−0.632216	−	0.251200i
$787$		−	14.3616i		−	0.511937i	−0.966685	−	0.255968i	$-0.917606\pi$
$787$		−	14.3616i		−	0.511937i	0.966685	−	0.255968i	$-0.0823943\pi$
$788$	−18.4892			−0.658649
$789$	1.59885	+	0.635278i	0.0569207	+	0.0226165i
$790$	24.4346			0.869345
$791$	18.7645			0.667188
$792$	−24.6347	−	13.0370i	−0.875355	−	0.463251i
$793$	58.1149			2.06372
$794$	28.6705			1.01748
$795$	44.6750	+	17.7509i	1.58446	+	0.629558i
$796$	32.5109			1.15232
$797$		−	37.2339i		−	1.31889i	−0.751752	−	0.659446i	$-0.770791\pi$
$797$		−	37.2339i		−	1.31889i	0.751752	−	0.659446i	$-0.229209\pi$
$798$	−4.67659	−	1.85816i	−0.165549	−	0.0657783i
$799$		−	0.0367077i		−	0.00129862i
$800$	5.64091			0.199436
$801$	5.31699	−	5.63453i	0.187866	−	0.199086i
$802$			1.97036i			0.0695758i
$803$	−3.08477	−	11.1606i	−0.108859	−	0.393849i
$804$	3.94826	+	1.56877i	0.139244	+	0.0553264i
$805$		−	14.0949i		−	0.496778i
$806$			24.4187i			0.860112i
$807$	8.91970	−	22.4489i	0.313988	−	0.790239i
$808$	8.32505			0.292874
$809$	−10.4350			−0.366876			−0.183438	−	0.983031i	$-0.558723\pi$
$809$	−10.4350			−0.366876			−0.183438	+	0.983031i	$0.558723\pi$
$810$	18.8754	−	1.09552i	0.663213	−	0.0384928i
$811$			22.1974i			0.779458i	0.920930	+	0.389729i	$0.127431\pi$
$811$			22.1974i			0.779458i	−0.920930	+	0.389729i	$0.872569\pi$
$812$			8.19699i			0.287658i
$813$	19.9016	−	50.0880i	0.697981	−	1.75666i
$814$	21.1360	−	5.84195i	0.740817	−	0.204760i
$815$		−	19.9075i		−	0.697329i
$816$	0.0295981	+	0.0117603i	0.00103614	+	0.000411694i
$817$	31.9739			1.11863
$818$			0.418621i			0.0146367i
$819$	11.3629	+	10.7225i	0.397053	+	0.374676i
$820$		−	8.77409i		−	0.306405i
$821$	29.0050			1.01228			0.506140	−	0.862451i	$-0.331072\pi$
$821$	29.0050			1.01228			0.506140	+	0.862451i	$0.331072\pi$
$822$	9.71346	−	24.4466i	0.338796	−	0.852674i
$823$	−9.36373			−0.326399			−0.163199	−	0.986593i	$-0.552181\pi$
$823$	−9.36373			−0.326399			−0.163199	+	0.986593i	$0.552181\pi$
$824$	5.90246			0.205622
$825$	5.64505	+	0.615132i	0.196535	+	0.0214161i
$826$	−1.90620			−0.0663251
$827$	−9.70831			−0.337591			−0.168795	−	0.985651i	$-0.553988\pi$
$827$	−9.70831			−0.337591			−0.168795	+	0.985651i	$0.553988\pi$
$828$	−14.9783	+	15.8728i	−0.520530	+	0.551618i
$829$	7.91149			0.274777			0.137389	−	0.990517i	$-0.456129\pi$
$829$	7.91149			0.274777			0.137389	+	0.990517i	$0.456129\pi$
$830$		−	32.9132i		−	1.14243i
$831$	5.53721	−	13.9359i	0.192084	−	0.483433i
$832$			24.2489i			0.840679i
$833$	−0.151573			−0.00525170
$834$	1.20581	−	3.03475i	0.0417538	−	0.105085i
$835$			6.47836i			0.224193i
$836$	3.77689	+	13.6647i	0.130626	+	0.472603i
$837$	−11.9904	−	25.7237i	−0.414449	−	0.889141i
$838$			14.2123i			0.490957i
$839$			25.0777i			0.865779i	0.901447	+	0.432890i	$0.142506\pi$
$839$			25.0777i			0.865779i	−0.901447	+	0.432890i	$0.857494\pi$
$840$	11.0340	+	4.38419i	0.380710	+	0.151269i
$841$	13.1192			0.452385
$842$	1.68085			0.0579260
$843$	−42.4187	−	16.8543i	−1.46098	−	0.580495i
$844$		−	19.4841i		−	0.670671i
$845$		−	34.5561i		−	1.18877i
$846$	−0.428059	+	0.453623i	−0.0147170	+	0.0155959i
$847$	−5.64918	−	9.43858i	−0.194108	−	0.324313i
$848$		−	1.37590i		−	0.0472486i
$849$	−16.9772	+	42.7279i	−0.582657	+	1.46642i
$850$	0.128624			0.00441176
$851$		−	44.3598i		−	1.52064i
$852$	−6.11603	+	15.3927i	−0.209532	+	0.527345i
$853$		−	30.3301i		−	1.03848i	−0.854628	−	0.519241i	$-0.826215\pi$
$853$		−	30.3301i		−	1.03848i	0.854628	−	0.519241i	$-0.173785\pi$
$854$	9.57985			0.327816
$855$	−18.0705	−	17.0521i	−0.617999	−	0.583170i
$856$	−43.6166			−1.49079
$857$	12.8728			0.439726			0.219863	−	0.975531i	$-0.429439\pi$
$857$	12.8728			0.439726			0.219863	+	0.975531i	$0.429439\pi$
$858$	−2.78209	+	25.5312i	−0.0949790	+	0.871620i
$859$	22.0184			0.751259			0.375629	−	0.926770i	$-0.377427\pi$
$859$	22.0184			0.751259			0.375629	+	0.926770i	$0.377427\pi$
$860$	−29.2008			−0.995738
$861$	1.81557	−	4.56940i	0.0618746	−	0.155725i
$862$	−13.1802			−0.448920
$863$			41.5594i			1.41470i	0.706865	+	0.707349i	$0.250109\pi$
$863$			41.5594i			1.41470i	−0.706865	+	0.707349i	$0.749891\pi$
$864$	−12.5275	−	26.8759i	−0.426193	−	0.914337i
$865$		−	7.41868i		−	0.252243i
$866$	−7.78285			−0.264472
$867$	−27.3270	−	10.8579i	−0.928073	−	0.368754i
$868$		−	6.89858i		−	0.234153i
$869$	−10.2770	−	37.1820i	−0.348624	−	1.26131i
$870$	8.71983	−	21.9459i	0.295630	−	0.744035i
$871$		−	10.1138i		−	0.342693i
$872$		−	11.7537i		−	0.398032i
$873$	−11.0421	−	10.4198i	−0.373720	−	0.352658i
$874$	−16.7340			−0.566037
$875$	9.81672			0.331866
$876$	2.82018	−	7.09776i	0.0952850	−	0.239811i
$877$		−	25.0341i		−	0.845341i	−0.906283	−	0.422671i	$-0.861093\pi$
$877$		−	25.0341i		−	0.845341i	0.906283	−	0.422671i	$-0.138907\pi$
$878$			3.29185i			0.111095i
$879$	−51.9468	−	20.6402i	−1.75212	−	0.696177i
$880$	−0.262310	−	0.949031i	−0.00884248	−	0.0319918i
$881$		−	17.9254i		−	0.603923i	−0.953320	−	0.301961i	$-0.902359\pi$
$881$		−	17.9254i		−	0.603923i	0.953320	−	0.301961i	$-0.0976414\pi$
$882$	1.87310	+	1.76754i	0.0630706	+	0.0595162i
$883$	−34.8036			−1.17123			−0.585617	−	0.810588i	$-0.699148\pi$
$883$	−34.8036			−1.17123			−0.585617	+	0.810588i	$0.699148\pi$
$884$		−	0.996988i		−	0.0335323i
$885$	−8.74646	−	3.47526i	−0.294009	−	0.116820i
$886$		−	6.46815i		−	0.217302i
$887$	−24.3669			−0.818159			−0.409079	−	0.912499i	$-0.634150\pi$
$887$	−24.3669			−0.818159			−0.409079	+	0.912499i	$0.634150\pi$
$888$	34.7267	+	13.7981i	1.16535	+	0.463033i
$889$	0.108701			0.00364573
$890$	−5.42505			−0.181848
$891$	−9.60590	−	28.2618i	−0.321810	−	0.946804i
$892$	22.7123			0.760463
$893$	0.819613			0.0274273
$894$	10.8314	+	4.30366i	0.362255	+	0.143936i
$895$	23.9812			0.801602
$896$		−	7.41586i		−	0.247747i
$897$	48.2819	+	19.1840i	1.61209	+	0.640536i
$898$			9.47917i			0.316324i
$899$	−35.4475			−1.18224
$900$	2.72412	+	2.57059i	0.0908039	+	0.0856865i
$901$		−	1.71909i		−	0.0572711i
$902$	7.79047	−	2.15327i	0.259394	−	0.0716960i
$903$	−15.2073	−	6.04235i	−0.506066	−	0.201077i
$904$			52.5632i			1.74823i
$905$		−	19.6520i		−	0.653256i
$906$	−4.51113	+	11.3535i	−0.149872	+	0.377195i
$907$	−5.80381			−0.192712			−0.0963562	−	0.995347i	$-0.530719\pi$
$907$	−5.80381			−0.192712			−0.0963562	+	0.995347i	$0.530719\pi$
$908$	−16.7860			−0.557062
$909$	6.48453	+	6.11908i	0.215078	+	0.202957i
$910$		−	10.9405i		−	0.362673i
$911$		−	36.4746i		−	1.20846i	−0.796812	−	0.604228i	$-0.793482\pi$
$911$		−	36.4746i		−	1.20846i	0.796812	−	0.604228i	$-0.206518\pi$
$912$	−0.262586	+	0.660870i	−0.00869508	+	0.0218836i
$913$	−50.0838	+	13.8431i	−1.65753	+	0.458138i
$914$		−	5.41698i		−	0.179178i
$915$	43.9565	+	17.4654i	1.45316	+	0.577388i
$916$	−24.4020			−0.806264
$917$		−	12.8269i		−	0.423582i
$918$	−0.285651	−	0.612824i	−0.00942788	−	0.0202262i
$919$		−	14.9130i		−	0.491934i	−0.969278	−	0.245967i	$-0.920895\pi$
$919$		−	14.9130i		−	0.491934i	0.969278	−	0.245967i	$-0.0791055\pi$
$920$	39.4826			1.30170
$921$	−1.09425	+	2.75399i	−0.0360568	+	0.0907470i
$922$	−2.93827			−0.0967669
$923$	39.4297			1.29784
$924$	0.785974	−	7.21287i	0.0258567	−	0.237286i
$925$	−7.61312			−0.250318
$926$	−4.27758			−0.140570
$927$	4.59753	+	4.33842i	0.151003	+	0.142493i
$928$	−37.0352			−1.21574
$929$			26.1737i			0.858730i	0.903131	+	0.429365i	$0.141263\pi$
$929$			26.1737i			0.858730i	−0.903131	+	0.429365i	$0.858737\pi$
$930$	−7.33860	+	18.4696i	−0.240642	+	0.605643i
$931$		−	3.38435i		−	0.110917i
$932$	5.60705			0.183665
$933$	5.10272	−	12.8424i	0.167056	−	0.420442i
$934$		−	1.21704i		−	0.0398227i
$935$	−0.327738	−	1.18575i	−0.0107182	−	0.0387781i
$936$	−30.0361	+	31.8299i	−0.981761	+	1.04039i
$937$		−	35.6941i		−	1.16607i	−0.812445	−	0.583037i	$-0.801864\pi$
$937$		−	35.6941i		−	1.16607i	0.812445	−	0.583037i	$-0.198136\pi$
$938$		−	1.66719i		−	0.0544357i
$939$	12.7960	+	5.08426i	0.417580	+	0.165919i
$940$	−0.748526			−0.0244142
$941$	33.7819			1.10126			0.550629	−	0.834750i	$-0.314388\pi$
$941$	33.7819			1.10126			0.550629	+	0.834750i	$0.314388\pi$
$942$	−13.0452	−	5.18327i	−0.425034	−	0.168880i
$943$		−	16.3505i		−	0.532445i
$944$			0.269374i			0.00876736i
$945$	5.37214	+	11.5252i	0.174756	+	0.374914i
$946$	−7.16623	−	25.9272i	−0.232994	−	0.842967i
$947$		−	31.3380i		−	1.01835i	−0.860664	−	0.509174i	$-0.829951\pi$
$947$		−	31.3380i		−	1.01835i	0.860664	−	0.509174i	$-0.170049\pi$
$948$	9.39554	−	23.6465i	0.305153	−	0.768003i
$949$	−18.1815			−0.590197
$950$			2.87193i			0.0931776i
$951$	−6.39103	+	16.0848i	−0.207243	+	0.521586i
$952$		−	0.424589i		−	0.0137610i
$953$	10.9252			0.353901			0.176951	−	0.984220i	$-0.443377\pi$
$953$	10.9252			0.353901			0.176951	+	0.984220i	$0.443377\pi$
$954$	−20.0468	+	21.2440i	−0.649039	+	0.687801i
$955$	46.8674			1.51659
$956$	−1.76221			−0.0569940
$957$	−37.0624	−	4.03863i	−1.19806	−	0.130550i
$958$	−20.5031			−0.662424
$959$	17.6915			0.571288
$960$	−7.28757	+	18.3412i	−0.235205	+	0.591959i
$961$	−1.16746			−0.0376598
$962$		−	34.4323i		−	1.11014i
$963$	−33.9738	−	32.0591i	−1.09479	−	1.03309i
$964$			19.4486i			0.626397i
$965$	−1.00374			−0.0323116
$966$	7.95896	+	3.16236i	0.256075	+	0.101747i
$967$			24.1608i			0.776959i	0.921457	+	0.388480i	$0.127000\pi$
$967$			24.1608i			0.776959i	−0.921457	+	0.388480i	$0.873000\pi$
$968$	26.4394	−	15.8245i	0.849796	−	0.508620i
$969$	−0.328082	+	0.825710i	−0.0105395	+	0.0265256i
$970$			10.6316i			0.341360i
$971$		−	55.1411i		−	1.76956i	−0.466006	−	0.884781i	$-0.654308\pi$
$971$		−	55.1411i		−	1.76956i	0.466006	−	0.884781i	$-0.345692\pi$
$972$	6.19772	−	18.6878i	0.198792	−	0.599412i
$973$	2.19619			0.0704065
$974$	−21.1347			−0.677201
$975$	3.29240	−	8.28623i	0.105441	−	0.265372i
$976$		−	1.35377i		−	0.0433332i
$977$			14.5912i			0.466815i	0.972379	+	0.233408i	$0.0749877\pi$
$977$			14.5912i			0.466815i	−0.972379	+	0.233408i	$0.925012\pi$
$978$	11.2412	+	4.46650i	0.359454	+	0.142823i
$979$	2.28174	+	8.25526i	0.0729246	+	0.263839i
$980$			3.09082i			0.0987325i
$981$	8.63924	−	9.15520i	0.275830	−	0.292303i
$982$	4.04778			0.129170
$983$			57.8582i			1.84539i	0.385530	+	0.922695i	$0.374019\pi$
$983$			57.8582i			1.84539i	−0.385530	+	0.922695i	$0.625981\pi$
$984$	12.7998	+	5.08580i	0.408044	+	0.162129i
$985$			35.8230i			1.14142i
$986$	−0.844475			−0.0268936
$987$	−0.389820	−	0.154888i	−0.0124081	−	0.00493015i
$988$	22.2609			0.708213
$989$	−54.4156			−1.73031
$990$	−9.77724	+	18.4750i	−0.310741	+	0.587174i
$991$	−16.5692			−0.526337			−0.263168	−	0.964750i	$-0.584767\pi$
$991$	−16.5692			−0.526337			−0.263168	+	0.964750i	$0.584767\pi$
$992$	31.1688			0.989610
$993$	53.9632	+	21.4414i	1.71247	+	0.680422i
$994$	6.49972			0.206159
$995$		−	62.9902i		−	1.99692i
$996$	−31.8516	−	12.6557i	−1.00926	−	0.401011i
$997$			54.6399i			1.73046i	0.501373	+	0.865231i	$0.332828\pi$
$997$			54.6399i			1.73046i	−0.501373	+	0.865231i	$0.667172\pi$
$998$	−11.9293			−0.377614
$999$	16.9074	+	36.2724i	0.534926	+	1.14761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.g.a.197.10	yes	24
3.2	odd	2	inner	231.2.g.a.197.15	yes	24
11.10	odd	2	inner	231.2.g.a.197.16	yes	24
33.32	even	2	inner	231.2.g.a.197.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.g.a.197.9	✓	24	33.32	even	2	inner
231.2.g.a.197.10	yes	24	1.1	even	1	trivial
231.2.g.a.197.15	yes	24	3.2	odd	2	inner
231.2.g.a.197.16	yes	24	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.858468 q^{2} +(1.60964 + 0.639565i) q^{3} -1.26303 q^{4} +2.44714i q^{5} +(-1.38183 - 0.549047i) q^{6} -1.00000i q^{7} +2.80121 q^{8} +(2.18191 + 2.05895i) q^{9} +O(q^{10})\)	\(q-0.858468 q^{2} +(1.60964 + 0.639565i) q^{3} -1.26303 q^{4} +2.44714i q^{5} +(-1.38183 - 0.549047i) q^{6} -1.00000i q^{7} +2.80121 q^{8} +(2.18191 + 2.05895i) q^{9} -2.10079i q^{10} +(-3.19676 + 0.883578i) q^{11} +(-2.03303 - 0.807792i) q^{12} +5.20778i q^{13} +0.858468i q^{14} +(-1.56511 + 3.93903i) q^{15} +0.121314 q^{16} +0.151573 q^{17} +(-1.87310 - 1.76754i) q^{18} +3.38435i q^{19} -3.09082i q^{20} +(0.639565 - 1.60964i) q^{21} +(2.74432 - 0.758524i) q^{22} -5.75973i q^{23} +(4.50895 + 1.79156i) q^{24} -0.988494 q^{25} -4.47072i q^{26} +(2.19527 + 4.70965i) q^{27} +1.26303i q^{28} +6.48993 q^{29} +(1.34359 - 3.38153i) q^{30} -5.46192 q^{31} -5.70656 q^{32} +(-5.71076 - 0.622291i) q^{33} -0.130121 q^{34} +2.44714 q^{35} +(-2.75583 - 2.60052i) q^{36} +7.70173 q^{37} -2.90535i q^{38} +(-3.33072 + 8.38268i) q^{39} +6.85495i q^{40} +2.83876 q^{41} +(-0.549047 + 1.38183i) q^{42} -9.44759i q^{43} +(4.03761 - 1.11599i) q^{44} +(-5.03853 + 5.33944i) q^{45} +4.94454i q^{46} -0.242178i q^{47} +(0.195273 + 0.0775883i) q^{48} -1.00000 q^{49} +0.848591 q^{50} +(0.243979 + 0.0969411i) q^{51} -6.57760i q^{52} -11.3416i q^{53} +(-1.88457 - 4.04308i) q^{54} +(-2.16224 - 7.82293i) q^{55} -2.80121i q^{56} +(-2.16451 + 5.44759i) q^{57} -5.57140 q^{58} +2.22046i q^{59} +(1.97678 - 4.97512i) q^{60} -11.1592i q^{61} +4.68888 q^{62} +(2.05895 - 2.18191i) q^{63} +4.65628 q^{64} -12.7442 q^{65} +(4.90250 + 0.534218i) q^{66} -1.94205 q^{67} -0.191442 q^{68} +(3.68372 - 9.27111i) q^{69} -2.10079 q^{70} -7.57130i q^{71} +(6.11199 + 5.76754i) q^{72} +3.49122i q^{73} -6.61169 q^{74} +(-1.59112 - 0.632207i) q^{75} -4.27454i q^{76} +(0.883578 + 3.19676i) q^{77} +(2.85932 - 7.19627i) q^{78} +11.6311i q^{79} +0.296873i q^{80} +(0.521482 + 8.98488i) q^{81} -2.43699 q^{82} +15.6670 q^{83} +(-0.807792 + 2.03303i) q^{84} +0.370921i q^{85} +8.11046i q^{86} +(10.4465 + 4.15073i) q^{87} +(-8.95480 + 2.47509i) q^{88} -2.58238i q^{89} +(4.32542 - 4.58374i) q^{90} +5.20778 q^{91} +7.27472i q^{92} +(-8.79175 - 3.49325i) q^{93} +0.207902i q^{94} -8.28197 q^{95} +(-9.18554 - 3.64972i) q^{96} -5.06076 q^{97} +0.858468 q^{98} +(-8.79429 - 4.65407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

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